Diagnostic checks in time series models based on a new correlation coefficient of residuals

Abstract

For checking time series models, the Ljung–Box, Li–Mak and Zhu–Wang statistics play an important role, which use the Pearson's correlation coefficient to implement (squared) residual (partial) autocorrelation tests. In this paper, we replace the Pearson's correlation coefficient with a new rank correlation coefficient and propose a new test statistic to conduct diagnostic checks for residuals in autoregressive moving average models, autoregressive conditional heteroscedasticity models and integer-valued time series models, respectively. We conduct simulations to assess the performance of the new test statistic, and compare it with existing ones, and the results show the superiority of the proposed one. We use three real examples to exhibit its usefulness.

Keywords:

• ARCH
• ARMA
• bootstrap
• INARCH
• Pearsons correlation coefficient
• rank correlation coefficient

Acknowledgments

The authors thank two referees for their useful and constructive comments on an earlier draft of this article.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Zhu's work is supported by National Natural Science Foundation of China (No. 12271206), Natural Science Foundation of Jilin Province (No. 20210101143JC), and Science and Technology Research Planning Project of Jilin Provincial Department of Education (No. JJKH20231122KJ). Li's work is supported by National Natural Science Foundation of China (No. 12201069), Natural Science Foundation of Jilin Province (No. 20210101160JC), Science and Technology Research Project of Jilin Provincial Education Department (No. JJKH20220820KJ) and Natural Science Foundation Projects of CCNU (CSJJ2022006ZK).